Question: Simplify. Rewrite the expression in the form $9^n$. $\dfrac{9^{7}}{9^5}=$
Explanation: $\begin{aligned} \dfrac{9^{7}}{9^5}&=9^{7-5} \\\\ &=9^2 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{9^{7}}{9^5}&=\dfrac{\overbrace{\cancel 9\cdot \cancel 9\cdot \cancel 9\cdot \cancel 9\cdot \cancel 9\cdot 9\cdot 9}^\text{7 times}}{\underbrace{\cancel 9\cdot \cancel 9\cdot \cancel 9\cdot \cancel 9\cdot \cancel 9}_\text{5 times}} \\\\\\ &=\underbrace{9\cdot 9}_\text{2 times} \\\\ &=9^2 \end{aligned}$ In conclusion, $\dfrac{9^{7}}{9^5}=9^2$.